Many years ago, newspapers occasionally mentioned "The Flat Earth Society". Their members persisted in their belief that our Earth is not a globe but a flat plane in space. And they offered many explanations to counter evidence for a curved Earth. (Maybe the Society still exists.)Our schools and colleges and media act as if we all are members of this Society. For one of the most quoted cliché is "A straight line is the shortest distance between two points."
This statement is INCOMPLETE. It should contain a conditional proviso such as "in Euclidean geometry" or "on a flat" or "on a plane". Try to verify it on a wheel.
On our curved Earth, "The shortest distance between two ground points on the Earth is an arc of a Great Circle of the Earth." These are indicated as latitudes on maps or globes of the Earth.
Another "piece of evidence" of "flat-earth thinking" in our schools, colleges, media is failure to report or comment on the following important historic achivement. (They have better information resources than I have!)
Prior to World War II, the old Henry Ford (x-y), founder of Ford Motors, directed the planning and construction of what became the longest production line in the world. It was so long that engineers could no longer ignore the curvature of the earth, but must take it into account in building this "straight" production line. Why? Because, otherwise, the gravitational effect of increasing distance from center of the Earth could make the production line bend or buckle, causing problems.
But this isn't the only problem created by what (elsewhere) I call "geobias". Even if this dictum "A straight line ..." were correct about the Earth on which we live, it would have this "primary" importance on in a Static World. In a dynamic world, we must concern ourselves with "the shortest travel-time between two ground points on the Earth". I'll explain by an example.Suppose you live on a major highway passing through a city. And you work in a building many miles down that same highway. After movimg car out of the garage beside you apartment building, you can drive "straight" up the highway, until you come to work place, and park in its garage. Is this the best way to go to work -- by a "straight line"?
Other think the same way, so -- beginning two hours before your usual dily departure -- the highway is clogged with cars, and you can travel at, say, an average speed of 20 MPH. But you discover an alternative. By turning right at the nearest cross street and driving down four long three long blocks, then turning left onto a street that parallels "your highway", you can usually get to work 15-30 minutes quicker. To do so, you must drive about a half-mile longer, but take less time to do so. What would you do?
In a Static World, we may value "shortest distances", but in a Dynamic World we may value "shortest times".
We were taught this lesson more than 300 years ago by Pierre de Fermat (1601-1665), the lawyer and judge who is considered "the greatest of amateur mathematicians". Independently of Newton and Lewibinitz, Fermat initiated the differential and integral claculus and is considered the greatest fo "number theorists" (in "higher arithmetic"). He initiated "Fermat's Last Theorem", which challanged mathematicians down to our time, when it was apparently first proven by the American Andrew Wiles.Fermat helped to found the physics of optics by a result which implies that light follows a path which minimizes the time of travel.
But our mentors and gabblers ignore this and talk as if we live in a Static World on a Flat